### Undirected connectivity in log-spaceUndirected connectivity in log-space

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 Author Reingold, Omer Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2008 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Derandomization ♦ Bounded space algorithms ♦ Pseudorandom generator Abstract We present a $\textit{deterministic},$ log-space algorithm that solves st-connectivity in undirected graphs. The previous bound on the space complexity of undirected st-connectivity was $log^{4/3}(ṡ)$ obtained by Armoni, Ta-Shma, Wigderson and Zhou (JACM 2000). As undirected st-connectivity is complete for the class of problems solvable by symmetric, nondeterministic, log-space computations (the class SL), this algorithm implies that SL = L (where L is the class of problems solvable by deterministic log-space computations). Independent of our work (and using different techniques), Trifonov (STOC 2005) has presented an $\textit{O}(log$ $\textit{n}$ log log $\textit{n})-space,$ deterministic algorithm for undirected st-connectivity. Our algorithm also implies a way to construct in log-space a $\textit{fixed}$ sequence of directions that guides a deterministic walk through all of the vertices of any connected graph. Specifically, we give log-space constructible universal-traversal sequences for graphs with restricted labeling and log-space constructible universal-exploration sequences for general graphs. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2008-09-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 55 Issue Number 4 Page Count 24 Starting Page 1 Ending Page 24

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Source: ACM Digital Library